Recently I started using a heart rate monitor during hill-climbing exercise. I noticed that when I stop to rest my heart rate goes up significantly before going back down. For example, if my heart rate is 138 when I begin to rest, 5-10 seconds later it will typically average above 145 for 10-15 seconds during which it will often spike as high as 158. After this it will begin to decrease and 30-40 seconds after the beginning of the rest period it will generally be below 120 and I will feel able to resume activity.

The research on heart rate recovery within 1 minute of exercise prompts this question. Measured 1 minute after exercise, there does not appear to be a problem. It is the intervening spike in heart rate that is mystifying.

I am a 58 year old male with general good health. I typically climb 400-800 vertical feet in each exercise session and have been doing this 3-5 times a week for 8-10 weeks.

What you describe is actually not at all unusual, and so long as it doesn't persist for more than a few minutes, is normal. What happens is that during recovery after exercise there frequently is a metabolic shift momentarily, as the residual adrenaline in the bloodstream "hits" while the body is trying to slow down. The brief and relatively mild "spike" you describe is normal for selected individuals so long as it does not persist beyond a minute or so. This is why recovery rate is checked beginning one to five minutes after a five-minute cooldown (which is a factor you didn't mention, and which can help eliminate this rebound effect). A cooldown is always recommended, but either way you seem to be managing the level of exercise intensity very well. Good work!